SOLUTION: what 2 numbers add to get -4 and multiply to get 3

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Question 1203982: what 2 numbers add to get -4 and multiply to get 3
Found 3 solutions by MathLover1, MathTherapy, josgarithmetic:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

let two numbers be and
if numbers add to get , we have
...eq.1

and if multiply to get , we have

...eq.2... solve for
..eq.2a

substitute in eq.1

...eq.1.. solve for , both sides multiply by

...factor


solutions:

or


go to
..eq.2a, substitute

or



so, solutions are
,
or
,



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
what 2 numbers add to get -4 and multiply to get 3

Creating equations to answer this is TOTALLY, TOTALLY UNNECESSARY. That's because one just needs to determine
which 2 INTEGERS have a PRODUCT of 3 (+ 3), and sum to - 4. If equations are created, it's the same thing the 
person has to do - if solving using the FACTORING method - unless of course, the person plans on using the
quadratic equation formula, which in this case, in my opinion, is TOTALLY, TOTALLY UNNECESSARY!! 

So, going back to the problem, 3 is PRIME, and so, its ONLY factors are 3 and 1. But, since (+ 3)(+ 1) = + 3, 
and also (- 3)(- 1) = + 3, it's clear that ONLY the factors, - 3 and - 1 SUM to - 4.

Therefore, the 2 integers being sought are  - 3 and - 1.
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Multiply to result in 3:
-1 & -3
1 & 3

Add the two numbers to result in -4:
Only ONE of those simple choices works.
-1 and -3.

---
If desired:
two numbers x and -4-x.






.
.
but the two numbers will be -1 and -3.
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